"there exist problems" is a correct and usable phrase in written English.
You can use it when you want to express that there are difficulties or issues to be addressed in a given situation. For example, "There exist problems with the recent budget proposal that need to be addressed before it is approved."
There exist problems in applications whose models can be written in the form [9]. (1.4).
There exist problems for which the most efficient known decision algorithm has exponential time complexity in the worst case (and in fact are known to be \ \textbf{NP}\ -hard in the general case – see Section 3.2) but which operate in polynomial time either in the average case or for a large subclass of problem instances of practical interest.
There exist problems in applications whose models can be written in the form [2] x ′ ( t ) − q ( t ) x ′ ( g ( t ) ) + ∑ i = 1 m b i ( t ) x ( h i ( t ) ) = f ( t ), t ∈ [ 0, ∞ ). (4). This equation is a particular case of (1).
It shows that there exist problems of inequality in health among older adults in the study setting.
The present study shows that there exist problems of inequality in health among older adults in the study setting.
But did there exist a legitimate problem that wasn't being addressed?
But, in nonconvex multiobjective optimization problem there exist no guarantee to existence dual elements for determining properly efficient solutions.
In any image segmentation problem, there exist uncertainties.
Here it is worthy of note that for the monoobjective problem there exist a number of different circuits with similar performance.
Unfortunately, there exists the problem that the classical maximum likelihood estimator for these models is sufficiently sensitive to outliers.
In underwater conditions, the signal channel is not stable and there exists multipath problem which can cause large localization errors when the traditional localization methods are used.
